Looks like the equation is
[tex]g(x) + x \cos(g(x)) = x^3[/tex]
Differentiate both sides with respect to x, using the chain rule on the left side:
[tex]g'(x) + \cos(g(x)) - x \sin(g(x)) g'(x) = 3x^2[/tex]
Solve for g'(x) :
[tex]g'(x) (1 - x \sin(g(x))) = 3x^2 - \cos(g(x)) \\\\ g'(x) = \dfrac{3x^2 - \cos(g(x))}{1 - x \sin(g(x))}[/tex]
When x = 0, we have
[tex]g'(0) = \dfrac{0-\cos(g(0))}{1-0\sin(g(0))} = \boxed{-\cos(g(0))}[/tex]
(This is all you can say without providing the value of g (0).)
A glass container can hold 216a^3 cubic cm of water. inside the glass container is a metallic cube with a volume of 64b^3 cubic cm. How much water you will be able to fill the glass container with the metallic cube inside? Express your answer in factored form.
Answer:
[tex]16(3a-2b)(4a^2+3ab+2b)[/tex]
Step-by-step explanation:
We will be able to fill the glass up to the amount of water possible to hold in the glass, minus the amount in the cube. This means it will be able to hold [tex]216a^3-64b^3=(6a)^3-(4b)^3[/tex]cubic cm of water.
Using the difference of cubes formula(you can prove this by expanding back out again), we get that [tex](6a^3)-(4b)^3=(6a-4b)((6a)^2+(6a)(4b)+(4b)^2)=(6a-4b)(36a^2+24ab+16b)=8(6a-4b)(4a^2+3ab+2b)=16(3a-2b)(4a^2+3ab+2b)[/tex]
Therefore, the answer is [tex]\boxed{16(3a-2b)(4a^2+3ab+2b)}[/tex] cubic centimeters and we're done!
Oh my oh why… Help maybe? Thanks
Answer:
Oh my oh my
Step-by-step explanation:
I don't know the answer
Answer:
426
Step-by-step explanation:
Middle Rectangle Volume:
3x7x6=126
2 Cube volumes:
5x5x6=150
150x2=300
Total Volume:
300+126=426
[tex](9x^2-42x+49)/(3x^2-7x)[/tex]
Help this is due today
Answer:
2 1/2 I think
Step-by-step explanation:
you find the L.C.M for all the fractions and multiply it. You should end up with whole numbers.
It should look like this
2n+3n=2
n= 2n+3n = 5
2 2
n= 2 1/2
For a test, please and thank you!
A babysitter gets
paid $60 for 4 hours
of work. How much
does he get paid
per hour?
Answer:
$15 per hour
Step-by-step explanation:
The babysitter got paid $60 in total for 4 hours of work
$60/4hr = $15/hr
Answer:
15$ per hour
Step-by-step explanation: If you divided 60 into 4 it is 15.
15x4=60
Find the least common multiple of 14 and 48.
Answer:
Find the least common multiple of 14 and 48=
336
Step-by-step explanation:
Answer:
The LCM of 14 and 48 is 336.
Step-by-step explanation:
14*48=672/2=336.
1; Multiply14 and 48=672
2; Simplify
3; Answer
Brainiest?
plz help someone!!!!!
Answer:
18
Step-by-step explanation:
The equation would be x^2+24^2=30^2. Solving would get 18.
Distributive property on 48x6=
Answer:
1×(480×6)
Step-by-step explanation:
ok it is distrutive property
Timmy is helping his grandpa on his chicken farm. Timmy has to pack 66 eggs into cartons, minimizing the packing cost. He can use 12-egg cartons and 6-egg cartons. Two 12-egg cartons cost as much as three 6-egg cartons.
The way to distribute the eggs at the lowest cost would be using 5 cartons of 12 eggs and 1 carton of 6 eggs.
Since Timmy is helping his grandpa on his chicken farm, and he has to pack 66 eggs into cartons, minimizing the packing cost, and he can use 12-egg cartons and 6-egg cartons, and two 12-egg cartons cost as much as three 6-egg cartons, to determine how many cartons of each should be used, the following calculation must be performed:
2 x 12 = 3 x 6 24 = 18 Thus, assuming as an example that a total of 2 cartons of 12 eggs and 3 cartons of 6 eggs cost $ 3, the value of each carton would be the following: 3/3 = 1 3/2 = 1.5 66/12 = 5.5 5 x 1.5 + 1 x 1 = X 7.5 + 1 = X 8.5 = X
In this way, the way to distribute the eggs at the lowest cost would be using 5 cartons of 12 eggs and 1 carton of 6 eggs.
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Question 9 of 10
Compute the slope of the line below. Enter your answer as a fraction or
decimal. Use a slash mark (1) as the fraction bar if necessary.
Help ASAP
Answer:
m= 1/8
Step-by-step explanation:
(-8,-8) (8,-6)
Use formula to calculate slope.
(y2-y1)/ (x2-x1)
Plug in coordinate point for x and y.
(-6-(-8))/(8-(-8))= 2/16= 1/8
17 EXPLORE students had a meeting about the latest trends in Machine Learning. Before the meeting started, they greeted each other, and each student hugged every other student. How many hugs occurred before the meeting?
The number of times an action is performed between every other person in a group can be calculated using the relation [tex] \frac{n(n - 1)} {2}[/tex] which is 136 times
Using the formular ;
[tex] \frac{n(n - 1)} {2}[/tex] n = number of persons = 17[tex] \frac{n(n - 1)} {2} = \frac{17(17 - 1)} {2}[/tex]
[tex] \frac{17(17 - 1)} {2} = \frac{17 \times 16} {2}[/tex]
[tex] \frac{17 \times 16} {2} = \frac{272}{2} = 136 [/tex]
Therefore, the all the 17 people present in the gathering hugged a total of 136 times
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Which shows the correct substitution of the values a, b, and c from the equation 1 = -2x + 3x + 1 into the quadratic
formula?
Quadratic formula x =
- b ± √b² - 400
20
O x= -(-2)V(-2)2 - 463)(0)
2 (3)
O x=-(-2) V(-2)2 - 4(3)(2)
2(3)
O x=-(-2) V(-2)2 – 43)(1)
23)
O x= -3132-4-2)(0)
2(-2)
Answer:
First option is the correct one because when we apply the equation given this is what is gives
The soil for house plants consists of 12% water. If someone wants to plant flowers
that need 28% water in the soil, how many liters of water they need to add to 5 kg of
soil?
The liters of water they need to add to 5 kg of soil is equal to
3.66 dl water.
We have given,
Anna bought soil that contains 12% of water.
She wants to plant a flower that needs 18% of water.
We have to determine, how much water does she need to pour in 5 kg of soil to plant the flower
Now, anna bought soil that contains 12% of water
5 kg of soil
Water = (12/100)2 = 0.6 kg
Let Water poured = W kg or liter
What is the total water?The addition of the amount of all water given in the question.
Therefore we get,
Total Water = 0.6 + W kg
Total Soil = 5 + W kg
18% of water
(18/100)(5 + W) = 0.6 + W
90 + 18W = 60 + 100W
30 = 82W
W = 30/82
W = 0.366 kg or 0.366 litre
or 3.66 dl
The liters of water they need to add to 5 kg of
soil is equal to 3.66 dl water.
To learn more about the mixture problem visit:
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ILL MARK BRAINLIEST
suppose y varies directly with x and y=4 when x=-2 find x when y=10
X=
Answer:
y= kx
when y = 4
x = -2
4= -2k
divide both sides by -2
k = -2
when y = 10
10 = x(-2)
10= -2x
divide both sides by -2
x = -5
Which expression is equivalent to -7(3h - 4) - 2?
Calculus, Limits and Continuity
Can someone please answer/explain this question? Thank you.
9514 1404 393
Answer:
(A) -4 and -2
Step-by-step explanation:
The constant in the function tells you f(0) = 5.
You know that the positive leading coefficient means the value of f(x) will be negative for x-values smaller than some number. The offered answer choices indicate the value x = -4 is a lower bound on the value of c. So, -4 < c < 0, for sure.
To further refine the interval, you would need to know f(-2) and/or f(-1).
f(-2) = (-2)³ -2(-2) +5 = -8 +4 +5 = 1
Then -4 < c < -2.
_____
I find a graphing calculator to be very helpful locating zeros of polynomials.
Help needed here please.
Answer:
a) -3 1/4
b) 4.3
c) -3 1/3
Step-by-step explanation:
Trigonometry table in LaTeX only.
No spam!
Answer:
[tex]\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\sf Trigonometry\: Table \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0 \end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}[/tex]
[tex]\Large{ \begin{tabular}{|c|c|c|c|c|c|} \cline{1-6} \theta & \sf 0^{\circ} & \sf 30^{\circ} & \sf 45^{\circ} & \sf 60^{\circ} & \sf 90^{\circ} \\ \cline{1-6} $ \sin $ & 0 & $\dfrac{1}{2 }$ & $\dfrac{1}{ \sqrt{2} }$ & $\dfrac{ \sqrt{3}}{2}$ & 1 \\ \cline{1-6} $ \cos $ & 1 & $ \dfrac{ \sqrt{ 3 }}{2} } $ & $ \dfrac{1}{ \sqrt{2} } $ & $ \dfrac{ 1 }{ 2 } $ & 0 \\ \cline{1-6} $ \tan $ & 0 & $ \dfrac{1}{ \sqrt{3} } $ & 1 & $ \sqrt{3} $ & $ \infty $ \\ \cline{1-6} \cot & $ \infty $ &$ \sqrt{3} $ & 1 & $ \dfrac{1}{ \sqrt{3} } $ &0 \\ \cline{1 - 6} \sec & 1 & $ \dfrac{2}{ \sqrt{3}} $ & $ \sqrt{2} $ & 2 & $ \infty $ \\ \cline{1-6} \csc & $ \infty $ & 2 & $ \sqrt{2 } $ & $ \dfrac{ 2 }{ \sqrt{ 3 } } $ & 1 \\ \cline{1 - 6}\end{tabular}}[/tex]
How do you solve this 18(6-c)+13c=123
Answer:
[tex]c = -3[/tex]
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
A pharmaceutical sales rep receives an 3.5% commission for selling
medication to physicians. If he sells $22,500 of medication, then how
much commission will he earn? *
Answer:
$787.50
Step-by-step explanation:
He will earn 22500*3.5/100 dollars. Simplifying will get 225*3.5, which is 787.5. So, he will get $787.50
If g(x)=3x-2, find g(3)-g(-8)
Answer:
33
Step-by-step explanation:
1. Let's solve for g(3)
Step 1: Plug in the value of x.
[tex]g(3)=3(3)-2[/tex]Step 2: Simplify.
[tex]g(3)=9-2[/tex] [tex]g(3)=7[/tex]2. Let's solve for g(-8)
Step 1: Plug in the value of x.
[tex]g(-8) = 3(-8)-2[/tex]Step 2: Simplify.
[tex]g(-8) = -24 - 2[/tex] [tex]g(-8)=-26[/tex]3. Now, let's subtract g(-8) from g(3).
[tex]g(3)-g(-8)[/tex] [tex](7)-(-26)[/tex] [tex]7+26[/tex] [tex]33[/tex]Therefore, the answer is 33.
Answer:
33
Step-by-step explanation:
g(x) = 3x - 2
g(3) = when x of g(x) function is 3.
g(3) = 3(3) - 2
g(3) = 9 - 2
g(3) = 7
g(-8) = 3(-8) - 2
g(-8) = -24 - 2
g(-8) = -26
g(3) - g(-8)
7 - (-26) = 33
A couple spent a total of $50.40 for dinner. This included a 20% tip and and 6% tax on the price meal. What was the price of the meal before tax and tip.
Answer:
50.40*（1-20%-6%）=50.4*0.74=37.296
Step-by-step explanation:
Evaluate this expression.
3^-2
Answer:Exact Form: one over 9
1
9
Step-by-step explanation: ,..
PLEASE READ CAREFULLY
Which of the following is true about linear functions? Select all that apply.
O There is exactly one output for each input.
O The graph of a linear function is a straight line.
O A linear function can cross the y-axis in two places.
O A linear function has a constant rate of change.
O A linear function must cross the x-axis.
I will mark Brainliest!
Answer:
B, DStep-by-step explanation:
A. There is exactly one output for each input.
False. This is incorrect for lines parallel to the x- axisB. The graph of a linear function is a straight line.
True.C. A linear function can cross the y-axis in two places.
False. Any line can cross another line once, never or overlap.D. A linear function has a constant rate of change.
True.E. A linear function must cross the x-axis.
False. The line may be parallel to the x-axis.Lets check
#1
False
for y=3 there are millions of same outputs as 3
#2
True
General equation y=mx+b
#3
No it's for higher degree functions
false
#4
True
constant is slope#5
False
SOMEBODY HELP ME AS SOON AS POSSIBLE !!
Answer:
387000000 (Question C)
Step-by-step explanation:
What is the mathematical answer to 365 x 2
Answer:
730
Step-by-step explanation:
Because when you add 365 and 365 together, you get 730
The mathematical answer to 365 x 2 is 1825.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given;
The mathematical expression; 365*5
Now,
=365*5
=1825
Therefore, by algebra multiplication will be 1825.
More about the Algebra link is given below.
brainly.com/question/953809
#SPJ5
Please help I’ll give 20 points
Answer:
__
4 -3.25 5 1.3 6 -3.33
Step-by-step explanation:
ye
A number is divisible by both 3 and 9. A number is missing.
1 5 5 _ 7
a. Both 0 and 3
b. Both 0 and 9
c. Only 3
d. Only 9
Answer:
l think that the answer is only 3. Hope this helps . IT'S LAURA RAYS AMIRA.pliz ,can you mark me the brainest.
What is the volume of a pool that is 10 feet long, 12 feet wide and 4 feet deep? Don’t forget unit
Answer:
480 feet.................